"Border guards... detected a drone trying to cross the border illegally" from Syria, it said in a statement, adding that the aircraft was "shot down over Jordanian territory".
The army said the drone was carrying "TNT-type explosive material".
Jordan often announces operations targeting the smuggling of arms and drugs from Syria, especially captagon, an amphetamine-like stimulant plaguing the Middle East.
It says smuggling has become "more organised", and that armed groups are now using drones.
On Sunday, the army said it shot down a drone flying from Syria that was loaded with crystal meth, the second such case in less than three weeks.
Several other interceptions of drones carrying arms and drugs from Syria were reported in February and June.
The vast majority of the region's captagon is produced in Syria and Lebanon and smuggled to its main consumer market in the Gulf.
Jordanian Foreign Minister Ayman Safadi and Syrian President Bashar al-Assad at a meeting in Damascus last month held talks on cooperation against drug trafficking.
Regional engagement with Assad's government has grown since its readmission to the Arab League in May, ending more than a decade of isolation after Syria's civil war erupted in 2011.
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